Extremal solutions of a class of dynamic boundary hemivariational inequalities

In this paper we consider a semilinear initial boundary value problem in a bounded cylindrical domain under flux conditions described by Clarke's generalized gradient of some locally Lipschitz function . Our main goal is to prove the existence of extremal solutions within a sector formed by a pair of appropriately defined upper and lower solutions when the function is of d.c. type, which means that can be represented as the difference of convex functions , . The main tools used in the proofs are results on nonlinear evolution equations, compact embeddings, comparison, truncation and regularization techniques.